相关论文: How much is optimal reinsurance degraded by error?

In a classical optimal stopping problem the aim is to maximize the expected value of a functional of a diffusion evaluated at a stopping time. This note considers optimal stopping problems beyond this paradigm. We study problems in which…

Maximum correntropy criterion regression (MCCR) models have been well studied within the frame of statistical learning when the scale parameters take fixed values or go to infinity. This paper studies the MCCR models with tending-to-zero…

This note studies the worst-case recovery error of low-rank and bisparse matrices as a function of the number of one-bit measurements used to acquire them. First, by way of the concept of consistency width, precise estimates are given on…

We consider distributed statistical optimization in one-shot setting, where there are $m$ machines each observing $n$ i.i.d. samples. Based on its observed samples, each machine then sends an $O(\log(mn))$-length message to a server, at…

Machine learning algorithms in high-dimensional settings are highly susceptible to the influence of even a small fraction of structured outliers, making robust optimization techniques essential. In particular, within the…

We study the problem of out-of-sample risk estimation in the high dimensional regime where both the sample size $n$ and number of features $p$ are large, and $n/p$ can be less than one. Extensive empirical evidence confirms the accuracy of…

A recent line of works, initiated by Russo and Xu, has shown that the generalization error of a learning algorithm can be upper bounded by information measures. In most of the relevant works, the convergence rate of the expected…

In this paper, we study convex risk measures with weak optimal transport penalties. In a first step, we show that these risk measures allow for an explicit representation via a nonlinear transform of the loss function. In a second step, we…

The escalating frequency and severity of natural disasters, exacerbated by climate change, underscore the critical role of insurance in facilitating recovery and promoting investments in risk reduction. This work introduces a novel Adaptive…

The issue of model risk in default modeling has been known since inception of the Academic literature in the field. However, a rigorous treatment requires a description of all the possible models, and a measure of the distance between a…

In the recent years, various gradient descent algorithms including the methods of gradient descent, gradient descent with momentum, adaptive gradient (AdaGrad), root-mean-square propagation (RMSProp) and adaptive moment estimation (Adam)…

Selecting appropriate regularization coefficients is critical to performance with respect to regularized empirical risk minimization problems. Existing theoretical approaches attempt to determine the coefficients in order for regularized…

Parameter fitting of data to a proposed equation almost always consider these parameters as independent variables. Here, the method proposed optimizes an arbitrary number of variables by the minimization of a function of a single variable.…

Robust optimization (RO) is a common approach to tractably obtain safeguarding solutions for optimization problems with uncertain constraints. In this paper, we study a statistical framework to integrate data into RO, based on learning a…

This paper deals with the problem of finding suboptimal values of an unknown function on the basis of measured data corrupted by bounded noise. As a prior, we assume that the unknown function is parameterized in terms of a number of basis…

The problem of parameterization is often central to the effective deployment of nature-inspired algorithms. However, finding the optimal set of parameter values for a combination of problem instance and solution method is highly…

In this paper, we propose a novel Mixed-Integer Non-Linear Optimization formulation to construct a risk score, where we optimize the logistic loss with sparsity constraints. Previous approaches are typically designed to handle binary…

Let A be an n by m matrix with m>n, and suppose that the underdetermined linear system As=x admits a sparse solution s0 for which ||s0||_0 < 1/2 spark(A). Such a sparse solution is unique due to a well-known uniqueness theorem. Suppose now…

Calibration, the practice of choosing the parameters of a structural model to match certain empirical moments, can be viewed as minimum distance estimation. Existing standard error formulas for such estimators require a consistent estimate…

This paper investigates a Pareto optimal insurance problem, where the insured maximizes her rank-dependent utility preference and the insurer is risk neutral and employs the mean-variance premium principle. To eliminate potential moral…